<group>
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H = <a href="%pathto:vl_harris;">VL_HARRIS</a>(I,SI) computes the Harris corner strength of the image I
at ``integration'' scale SI.
</p><p>
The Harris strength [1] of a pixel is a statistic of the gradient
of the image integrated in a neighborhood of that pixel. This
neighborhood is a Gaussian window of variance SI.
</p><p>
In computing the Harris corner strength, there is a second scale
parameter, the ``derivation'' scale SD, which is the variance of
the Gaussian kernel used to pre-smooth the image I before computing
its gradient. SI and SD are independent parameters and <a href="%pathto:vl_harris;">VL_HARRIS</a>(I,SI)
assumes that I is already smoothed at level SD.
</p><p>
<a href="%pathto:vl_harris;">VL_HARRIS</a>(I,SI) uses Noble's variation [2] of the Harris score. If
SIGMAP and SIGMAM are respectively the biggest and smallest
eigenvalue of the structure tensor at a pixel, the score is given
by (SIGMAP*SIGMAM) / (SIGMAP+SIGMAM/2).  Let GAMMA = SIGMAM/SIGMAP
the ratio between the eigenvalues, which measures the degree of
anisotropy of the tensor and is always comprised in the range
[0,1].  Noble's score can be decomposed in two factors: the biggest
eigenvalue SIGMAP and the number
</p><pre>
  RHO = (2 GAMMA) / (GAMMA + 1).
</pre><p>
RHO is another measure of isotropy that has value one for a
symmetric tensor and and zero for maximally anisotropic tensor.
[H,DETAILS] = <a href="%pathto:vl_harris;">VL_HARRIS</a>(I,SIGMA) returns the additional structure
DETAILS with the following fields:
</p><pre>
  DETAILS.SIGMAP
  DETAILS.RHO
</pre><p>
<a href="%pathto:vl_harris;">VL_HARRIS</a>(I,SI,ALPHA) uses Harris' original score [1], defined to be
SIGMAP*SIGMAM - ALPHA*(SIGMAP+SIGMAM)^2. This can be decomposed in
the factors SIGMAP^2 (note the square) and
</p><pre>
  RHO = GAMMA - ALPHA (1+GAMMA)^2.
</pre><p>
Note that RHO is equal to -ALPHA for a maximally anisotropic
tensor. Typically ALPHA=0.04 and this is what is used by
<a href="%pathto:vl_harris;">VL_HARRIS</a>(I,SI,[]).
</p><p>
REMARK. The gradient of the image I, used to compute the structure
tensor, is computed using central differencies. This means that a
function line [+1,-1,+1,...] has null Harris' score. This is
generally assumed to be a sampling artifact, and might be
avoided by oversampling the image.
</p><dl><dt>
EXAMPLE
</dt><dd><p>
To extacts Harris points from image I:
</p><pre>
  idx = vl_localmax( vl_harris( vl_imsmooth( I, sd ), si ) ) ;
  [i,j] = ind2sub( size(I), idx )
</pre></dd><dt>
REFERENCES
</dt><dd><p>
[1] C. Harris and M. Stephens, &quot;A combined corner and edge detector,&quot;
in Proceedings of The Fourth Alvey Vision Conference, pp. 147-151,
1988.
</p><p>
[2] J. A. Noble, &quot;Finding corners, &quot;Image Vision Computing, vol. 6,
no. 2, pp. 121-128, 1988.
</p></dd></dl><p>
See also: <a href="%pathto:vl_help;">VL_HELP</a>().
</p></div></group>
